Abstract

We have constructed an anti-Simpson's quadrature formula using Simpson's $\frac{1}{3}rd$ quadrature formula following the idea given by D. P. Laurie. An extension of this formula is developed by taking average linear combination with the Simpson's $\frac{1}{3}rd$ quadrature formula. Through error analysis, we studied the theoretical dominance of this extended anti-Simpson's quadrature formula over its constituents. We accomplished numerical verification of the formula evaluating test integrals including elliptic ones. We depict the novelty of the formula in both non-adaptive and adaptive environments. In adaptive environment the dominancy of the rule over its constituents clarifies both in number of steps and error committed.

Keywords and Phrases

Simpson's $\frac{1}{3}rd$ quadrature formula $(Q_{S_{3}}(f))$ , Anti-Simpson's 4-point quadrature formula $(Q_{aS_{4}}(f))$ , Extended anti-Simpson's quadrature formula $(DS_1(f))$ , Adaptive integration scheme, Elliptic integrals.

A.M.S. subject classification

Primary 65D30, 65D32, Secondary 65E05, 65A05.

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